Bill and Melinda Gates handed the world a report card last week, assessing its progress on 18 global health indicators: infant mortality, AIDS, vaccine use, smoking rates and so on.

Called “Goalkeepers,” the report was a huge statistical effort, three years in the making, aimed squarely at the world leaders gathering at the United Nations General Assembly this month. To draw extra attention to it, the Gateses will hold an awards dinner and a public release this week featuring former President Obama.

In a series of recent interviews, they delivered several messages.

Progress has been great, but donor fatigue could be lethal to millions who could easily be saved. Only the United States is rich enough and generous enough to lead, and private charities, including theirs, cannot possibly cover the deep cuts in global aid that President Trump has proposed.

Health journalists are sunk in negativism, they say, focusing on failures in a sea of global health successes.

In conversation, Mr. Gates displays such a deeply impressive grasp of the science fueling the discoveries he underwrites, and of the politics of the countries where they are deployed, that one forgets he was once a software geek.

At 61, he could speak with the avuncular magniloquence of a professor emeritus; instead, he layers on supporting data like a star pupil seeking an A-plus. He rebuts skeptical inquiries and insists on teaching from his own syllabus — and on flicking his own birch switch.

The report card will be issued annually, Mr. Gates said. He gave himself only a C+ on the first draft, promising sharper analytics in the future.

He isn’t actually handing out grades to the world’s health authorities — but is sending them home with a note for mom. Your kid has real potential but is becoming a discipline problem.

In some areas, like infant mortality, he considers the progress made “pretty miraculous.” In 1990, more than 11 million children died before their fifth birthday; now, fewer than 6 million do.

AIDS deaths have plummeted since 2004, and malaria deaths since 2005. Rates of childhood stunting, mothers dying in childbirth, and the miseries wrought by rare tropical diseases all have gone steadily down.

In poor countries, vaccine use is way up, though only about 75 percent of children get all the shots they need. More people have toilets these days.

Progress in other areas has been slower. Smoking is down, but tobacco companies are fighting back. Contraceptive availability is up, but almost half the women who want birth control still lack it.

Access to basic health care is up, according to the new report. But the gap between rich and poor countries remains vast, because too much money goes to top hospitals instead of rural clinics.

One key finding: Most of the progress was not bought by donors, but came organically as hundreds of millions of people scrambled out of the most abject tiers of penury.

In 1990, 35 percent of the world lived below the international poverty line (currently $1.90 a day); now, only 9 percent do. Most of the great leap upward was in just two economic powerhouses: China and India.

The report’s scarier themes lie in its projections for the next 15 years.

Assuming economic progress continues, improvements in most health categories will churn dutifully on, or at worst plateau. But since the 2008 economic crisis, donors have been losing their will to give.

If that persists, the report says, chaos threatens. H.I.V. infections could double, returning to levels not seen since the 1990s. And malaria could climb back to the peak hit in 2005.

H.I.V. and malaria are particularly vulnerable to fluctuations in funding because they are concentrated in Africa, where economic progress has been slower than in Asia or Latin America and where birthrates remain high, producing a big pool of potential victims each year. Malaria has a history of rebounding as soon as pressure is eased; both the mosquitoes and the parasites quickly evolve resistance genes.

The world’s birthrate is now peaking — probably forever — at about 134 million babies a year. “But it’s mind-blowing how much the shift in where kids are being born makes things hard for us,” Mr. Gates said.

Keeping infants alive gets tougher when they are born in lands with civil wars, dirt roads and healers who reject Western medicine.

Surprisingly, the new report was not a reaction to Mr. Trump’s threats to slash the foreign aid budget by 32 percent.

According to Dr. Christopher J.L. Murray, director of the University of Washington’s Institute for Health Metrics and Evaluation, which gathered the data, it was initiated three years ago because Mr. Gates feared the world was losing its focus on health.

“Goalkeepers” refers to a metric that the world ignores but the Gateses do not: the targets periodically set by the United Nations, namely the 2000 Millennium Development Goals and the 2015 Sustainable Development Goals.

The first sharply emphasized poverty and health. But the latter comprise 169 targets for everything from reducing overfishing to bringing clean energy and decent jobs for all — they have an “I-want-a-pony-too” air about them.

The world prefers simple goals, like declaring war on smallpox. But war talk has stung Mr. Gates. Calls for an “AIDS-free generation” – all the rage six years ago — were “premature,” he said, and he was “embarrassed” by claims that malaria could be eliminated by 2015.

He prefers “Microsoft-type thinking” to set realistic goals. “People expect a certain degree of honesty,” he said. “They want to know, do Bill and Melinda track this stuff?”

Essentially, he is tracking the world’s pursuit of his own goals as he helps it reach them.

In early interviews, Mr. Gates refrained from criticizing Mr. Trump but gave the clear impression that he believed Congress would ignore most of the president’s proposed cuts. Congress appears to be doing just that.

To hear Mr. Gates tell it, even the staunchest backers of an America First ideology, which he called “selfish,” succumb to his fusillades of data.

Before Stephen K. Bannon, the president’s chief strategist, resigned, Mr. Gates met him in the White House. “He said, ‘Africa has always been a mess,’” Mr. Gates said. “I went through the numbers on its progress with him. He was impressed.”

The new report’s weakness is that it cannot, for example, foretell how many more Ugandans would die of AIDS if American donations dropped 20 percent, in the way that the Congressional Budget Office can calculate how many Americans will lose insurance under a particular health care bill.

There are too many unpredictables in global health. A country would not just brutally take 20 percent of its H.I.V. patients off treatment, Mr. Gates noted. It might cut its military budget; it might try to stretch supplies of the drugs it got, triggering shortages.

Buried in the graphics-heavy report are some fun anecdotes that show how ingenuity can be just as important in the field as money.

In Ethiopia, for example, pregnant women were given a special stretcher to help them reach birth clinics; they had feared regular stretchers because villagers carried away on them usually died.

And an imam in Senegal described how he got other imams to accept birth control: by citing a saying from the Prophet Muhammad implying that children should be born about two years apart.